Phobos does eclipse the Sun on Mars, but these are just annular eclipses in which the full disk of the Sun is not blocked. Although these happen twice each Martian day, they are of very short duration. Deimos is so small that when it passes between Mars and the Sun, it looks like a sunspot, and there's not that much reduction in solar intensity at the surface of Mars. It's more proper to say that Diemos transits the Sun rather than eclipses it.

Because of its large size, the Moon has a present influence on terrestrial life because of its cycle of night time illumination over a period of the lunar month. There have been several studies showing lunar rhythms in aquatic animals.[5] A 1958 study showed evidence for lunar periodicity in the breeding of the scallop.[6]

Closer to home, it's quite apparent that the period of the human menstrual cycle matches the lunar month. A 1980 study showed that for a sample of 312 women, the mean and median of the menstrual cycle was 29.5 days, or exactly a lunar month.[8] Not only that, but the cycles were found to be in phase with the lunar month. Thirty percent of women have a menstrual cycle within a day of 29.5 days, and these tend to ovulate in the dark phase of the lunar period.[8] A follow-up study in 1987 showed that that such women tend to menstruate when the moon is full with a reduced probability of the onset of menses after the full moon.[9]

They found that at the time of the full moon, the EEG delta-wave activity during NREM sleep, which is an indicator of deep sleep, decreased by 30%. The time to fall asleep increased by five minutes, and the duration of sleep, as assessed by EEG, was reduced by twenty minutes.[10-13] These changes were associated with diminished endogenous melatonin levels,[10] and the study subjects assessed their own sleep as being poorer during the full moon.[11]

BiologistChristian Cajochen, the lead author of the study, is quoted in Science as saying, "A lot of people are going to say, 'Yeah, I knew this already. I never sleep well during a full moon.' But this is the first data that really confirms it... There had been numerous studies before, but many were very inconclusive."[13] Cajochen is further quited by BBC News as saying, "The lunar cycle seems to influence human sleep, even when one does not 'see' the Moon and is not aware of the actual moon phase."[12]

One of the most interesting aspects of the study is that it wasn't designed to detect lunar rhythms of sleep. The lunar correlation was done retrospectively using older sleep data.[12] These data were collected between 2000 and 2003, and the idea of looking for lunar rhythms was hatched by the scientists while visiting a pub during a full moon.[13] Neuroscientist, Kristin Tessmar-Raible of the Max F. Perutz Laboratories in Vienna, is quoted in Science as saying, "What's nicest about this study is that it uses data that wasn't originally intended for this purpose, so you know there couldn't be any bias and that makes it quite convincing."[13]

Another interesting aspect of the study is that the study subjects couldn't see the moon, so enhanced night time illumination is not the cause. It appears that this is a biological clock internal to humans, a relic of our ancestors, maintained through internal hormones.[13] The study data were not collected over a lunar month for any single study subject, which is something that might be tackled in follow-up experiments.[13]

References:

"It is often said that all the conditions for the first production of a living organism are now present, which could ever have been present.— But if (& oh what a big if) we could conceive in some warm little pond with all sorts of ammonia & phosphoric salts,—light, heat, electricity &c present, that a protein compound was chemically formed, ready to undergo still more complex changes, at the present day such matter wd be instantly devoured, or absorbed, which would not have been the case before living creatures were formed." (Letter to J. D. Hooker, February 1, 1871)